DFT characterization of the first step of methyl acrylate polymerization: Performance of modern functionals in the complete basis limit Ilhan Yavuz a,1 , Gökçen Alev A. Çiftçiog ˘lu b,1 a Department of Physics, Marmara University, 34722 Istanbul, Turkey b Department of Chemical Engineering, Marmara University, 34722 Istanbul, Turkey article info Article history: Received 13 August 2011 Received in revised form 27 September 2011 Accepted 28 September 2011 Available online 8 October 2011 Keywords: Density functional theory Free-radical polymerization Focal point analysis Hindered rotor approximation Methyl acrylate abstract We obtain values of the reaction barrier for the reaction of methyl acrylate CH 2 @CHCOOCH 3 (MA) with the radical CH 3 CHCOOCH 3 (HMA Å ) by density functional theory (DFT) using a variety of functionals and basis sets. Structures for the reactants and the transition state are optimized in B3LYP/cc-pVTZ. We extrapolate energies for these structures to the complete basis set (CBS) limit for each of the functionals B3LYP, PBE, TPSS, BMK, HSE2PBE, mPW1PW91, B97-1, wB97-XD, and M06-2X. The extrapolation follows the energies obtained by the basis sets cc-pVnZ with n = 2, 3, and 4. The estimate of the barrier height is sensitive to the basis and the choice of functional. In order to recover the rate constant for the radical addition we require partition functions as well as the barrier height. To obtain the partition functions for internal rotation in MA, the radical HMA Å , and the transition state for their addition HMAMA Å (TS), we trace one-dimensional torsional potentials in B3LYP/ cc-pVTZ. Using this data we employ a range of approximations to the partition function ranging from the harmonic oscillator limit, interpolation schemes linking the harmonic oscillator and free rotor limits, and semi-classical expressions. Comparison with the partition functions obtained by direct sum of Boltzmann factors with energy eigenvalues obtained by solution of the Schrödinger equations (total eigenvalue sum or TES) for the one-dimensional torsional potentials show that Mielke and Truhlar’s TDPPI-HS approxi- mation is very accurate. Estimates of activation energies and rate constants for the addition reaction based on the modern func- tionals wB97-XD and M06-2X in the CBS limit and the TES partition functions reproduce the best exper- imental measurement. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Free radical addition has generally been described within the absolute rate theory [1], which represents the rate according to kðT Þ¼ k B T h Q z Q M Q R e DE z 0 =RT ð1Þ The reaction barrier DE z 0 and partition functions for the acti- vated complex Q à , the monomer Q M , and the radical Q R are required to evaluate this expression. Quantum chemical methods can give all the information necessary for evaluation of the rate constant under the assumptions that: (1) energy is separable into terms dealing with rotation, vibration, and electronic contributions; (2) vibrations are separable into normal modes of motion; and (3) nu- clear motion takes place on a single potential surface defined by the electronic energy of a single state. The model for radical polymerization is that (1) an initiator I 2 is decomposed by heat or light to radicals I Å . (2) The radical adds to a monomer M to form the first of a sequence of larger radicals IM 1 Å . (3) Propagation extends the chain length according to M + IM j Å ? IM j+1 Å . These addition reactions are called ADj in the work we describe below. Finally (4) termination ends the growth of the polymer, either by a coupling reaction or by dispropor- tionation. Most attention has been given to the first few propagation steps. For methyl acrylate the minimal model of the first propaga- tion step AD1 involves the species shown in Fig. 1, in which MA is the monomer, HMA Å represents the radical and the transition state geometry is represented by HMAMA Å (TS). The initiation step has not been overlooked. Dossi et al. [2] studied the addition of initiating radicals methyl (Me Å ), phenyl (Ph Å ), benzoyl (BzO Å ), tert-butoxy (tBuO Å ), and 2-cyanoprop-2-yl (CNP Å , derived from 2,2 0 -azoisobutyronitrile, called AIBN) to the monomers methyl acrylate (MA), methyl methacrylate (MMA), acrylonitrile, and styrene. They find reasonable agreement with experimental enthalpies and activation energies for the addition 2210-271X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.comptc.2011.09.043 E-mail addresses: ilhan.yavuz@marmara.edu.tr (I. Yavuz), gciftcioglu@marmara. edu.tr (Gökçen Alev A. Çiftçiog ˘lu) 1 Co-authors. Computational and Theoretical Chemistry 978 (2011) 88–97 Contents lists available at SciVerse ScienceDirect Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc